Kullback–Leibler Divergence-Based Distributionally Robust Chance-Constrained Programming for PV Hosting Capacity Assessment in Distribution Networks

Chao Shen, Haoming Liu (liuhaom@hhu.edu.cn), Jian Wang, Zhihao Yang and Chen Hai
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Chao Shen: School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China
Haoming Liu: School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China
Jian Wang: School of Electrical and Power Engineering, Hohai University, Nanjing 211100, China
Zhihao Yang: College of Electrical, Energy and Power Engineering, Yangzhou University, Yangzhou 225000, China
Chen Hai: College of Artificial Intelligence and Automation, Hohai University, Nanjing 211100, China

Sustainability, 2025, vol. 17, issue 5, 1-23

Abstract: This paper addresses the challenge of assessing photovoltaic (PV) hosting capacity in distribution networks while accounting for the uncertainty of PV output, a critical step toward achieving sustainable energy transitions. Traditional optimization methods for dealing with uncertainty, including robust optimization (RO) and stochastic optimization (SO), often result in overly conservative or optimistic assessments, hindering the efficient integration of renewable energy. To overcome these limitations, this paper proposes a novel distributionally robust chance-constrained (DRCC) assessment method based on Kullback–Leibler (KL) divergence. First, the time-segment adaptive bandwidth kernel density estimation (KDE) combined with Copula theory is employed to model the conditional probability density of PV forecasting errors, capturing temporal and output-dependent correlations. The KL divergence is then used to construct a fuzzy set for PV output, quantifying its uncertainty within specified confidence levels. Finally, the assessment results are derived by integrating the fuzzy set into the optimization model. Case studies demonstrate its effectiveness of the method. Key findings indicate that higher confidence levels reduce PV hosting capacities due to broader uncertainty ranges, while increased historical sample sizes enhance the accuracy of distribution estimates, thereby increasing assessed capacities. By balancing conservatism and optimism, this method enables safer and more efficient PV integration, directly supporting sustainability goals such as reducing fossil fuel dependence and lowering carbon emissions. The findings provide actionable insights for grid operators to maximize renewable energy utilization while maintaining grid stability, advancing global efforts toward sustainable energy infrastructure.

Keywords: Copula theory; distributionally robust chance-constrained; kernel density estimation; Kullback–Leibler divergence; renewable energy integration (search for similar items in EconPapers)
JEL-codes: O13 Q Q0 Q2 Q3 Q5 Q56 (search for similar items in EconPapers)
Date: 2025
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